The generator matrix

 1  0  0  0  1  1  1  1 3X X+2  1  1  1  X 2X  1 X+2 3X+2  0 2X+2 2X+2  1  1  1  1  1  1 3X  1  0  1 2X  2  1  1  1  2 3X 3X  1  1  1  1  1  1 2X+2  1  2  1 2X  1  1  1 3X+2 2X  1 2X  1 2X  X  0 3X 3X  1  1 3X+2  1 X+2  1  1  1  1  1  1 X+2 3X 3X  1 X+2  1 X+2  1  1 3X+2  1 X+2  1
 0  1  0  0  0 2X+3 2X 3X+3  1  2  2  3 X+3  1  1 X+2  1  1  1  1 3X X+3  1 2X 3X+2  0 3X+3  X  3  X  0  2  1  X X+3 X+3  1  1 2X  2 3X+1  X  3 3X+3 3X  1  X  X 2X+3  1 X+1 3X+3 X+2  0 3X+2 3X  1 X+2  1  1  1 X+2 2X+2  X 2X+2  1 X+1  1  0  2  1 3X 2X X+1  1  1 2X  2 2X 3X+2  1 2X+2  1  X 2X+3  1 X+2
 0  0  1  0  2 2X+2 2X+3  1 X+3  1 2X+1  3  X  X 3X+3  X  2  1 3X  3 2X+2 X+1  X 2X+2 2X+1 3X+1 X+3  1  X  1 3X 3X+2 2X+3  2  3 2X+2  2 X+3  1  2 X+1  3 3X  0 3X+2 X+1 X+3  1  1 2X  X 3X+2 X+2  X  1 3X+3 X+3  X 2X+3 2X+2 2X+2  X  1 3X+1 3X+2 3X  0 3X+3 X+3 3X+1 2X+3 3X 3X+2 2X+2  X 3X+3  1 X+2  1  0 2X+1  0 2X+2  1 X+3 2X+3 2X
 0  0  0  1 X+3 3X+1 X+1 3X+3  X X+3 X+2 X+2 2X X+3  1 3X+2 3X+1 3X X+2  1  1 3X  0 2X+1 2X+1 2X X+1 X+2  1 2X+1 3X+2  1 3X+3 2X+3  3  X 2X+3 2X+2 2X+1 3X  2 X+1  X  1 2X 2X 3X X+2  1  X 3X+3 3X 3X+3  1 2X  1 X+3  1 2X+2  3 3X+1  1 3X+1 3X+1 X+3 3X+1 2X+3 3X  2  X X+1  0 2X X+1  0 2X+3 3X 2X+1  3 3X+3  2 2X+2  X  0  2 X+3 2X+1
 0  0  0  0 2X 2X 2X 2X  0  0 2X 2X 2X  0  0 2X  0  0  0  0  0 2X 2X 2X 2X 2X 2X  0 2X  0 2X  0  0 2X 2X 2X  0 2X 2X  0  0  0  0  0  0 2X  0 2X  0 2X  0  0  0 2X 2X 2X 2X  0 2X 2X 2X 2X 2X  0  0 2X 2X 2X  0  0  0 2X  0  0  0 2X 2X 2X  0  0  0 2X  0  0 2X 2X  0

generates a code of length 87 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 79.

Homogenous weight enumerator: w(x)=1x^0+534x^79+1909x^80+3704x^81+5657x^82+8204x^83+10306x^84+13048x^85+14255x^86+15716x^87+15033x^88+13158x^89+10532x^90+7690x^91+5165x^92+3226x^93+1529x^94+772x^95+277x^96+154x^97+66x^98+66x^99+27x^100+22x^101+8x^102+10x^103+1x^106+2x^108

The gray image is a code over GF(2) with n=696, k=17 and d=316.
This code was found by Heurico 1.16 in 203 seconds.